Temporal high-order rotated-staggered-grid finite difference method of anisotropic media elastic wave equations

WanLai LI, QianJin ZHAO, Hui WEI, YiXuan WANG

Prog Geophy ›› 2026, Vol. 41 ›› Issue (1) : 289-310.

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Prog Geophy ›› 2026, Vol. 41 ›› Issue (1) : 289-310. DOI: 10.6038/pg2026JJ0228

Temporal high-order rotated-staggered-grid finite difference method of anisotropic media elastic wave equations

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Abstract

When numerically simulating the elastic wave field in anisotropic media using the rotated staggered grid finite difference method, numerical dispersion phenomena usually occur. To solve this problem, a time-domain high-order difference coefficient calculation model based on the coupling of Taylor expansion and sampling approximation method is proposed, and an improved space-time domain high-order rotating staggered grid scheme is constructed. To verify the performance of the modified algorithm, the improved algorithm is compared with the general staggered grid and other rotated staggered grids, and the dispersion degree and stability of each algorithm are analyzed. Through the results of numerical experiments, it is found that the algorithm improved by the optimization strategy of the difference operator coefficients based on the Taylor expansion and the sampling approximation method can significantly suppress the dispersion of the elastic wave field in isotropic media, VTI/TTI anisotropic media, and the modified BP model.

Key words

Elastic wave equation / Finite-difference method / Rotated-staggered-grid / Dispersion analysis

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WanLai LI , QianJin ZHAO , Hui WEI , et al. Temporal high-order rotated-staggered-grid finite difference method of anisotropic media elastic wave equations[J]. Progress in Geophysics. 2026, 41(1): 289-310 https://doi.org/10.6038/pg2026JJ0228

References

List( Publishing order | Descend order by publishing year | Descend order by cited within ) Chart analysis
Almquist M , Dunham E M . Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions. Journal of Computational Physics, 2021, 424: 109842.
https://doi.org/10.1016/j.jcp.2020.109842
Cited in this article [1]
Behera L . Elastic anisotropic finite-difference full-wave modeling and imaging of 2D tilted transversely isotropic (TTI) media. Journal of Applied Geophysics, 2022, 207: 104837.
https://doi.org/10.1016/j.jappgeo.2022.104837
Cited in this article [1]
Chen H , Wang X M , Zhao H B . A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer. Chinese Science Bulletin, 2006, 51 (19): 2304- 2314.
https://doi.org/10.1007/s11434-006-2127-8
Cited in this article [2]
Doostaki R , Hosseini M M , Salemi A . A new simultaneously compact finite difference scheme for high-dimensional time-dependent PDEs. Mathematics and Computers in Simulation, 2023, 212: 504- 523.
https://doi.org/10.1016/j.matcom.2023.05.008
Cited in this article [1]
Fei T , Larner K . Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport. Geophysics, 1995, 60 (6): 1830- 1842.
https://doi.org/10.1190/1.1443915
Cited in this article [1]
Gao K , Huang L J . An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media. Journal of Computational Physics, 2017, 350: 361- 386.
https://doi.org/10.1016/j.jcp.2017.08.053
Cited in this article [2]
Gold N , Shapiro S A , Burr E . Modelling of high contrasts in elastic media using a modified finite difference scheme.//SEG Technical Program Expanded Abstracts. SEG, 1997, 1850- 1853.
Cited in this article [1]
Khan I R , Ohba R . Taylor series based finite difference approximations of higher-degree derivatives. Journal of Computational and Applied Mathematics, 2003, 154 (1): 115- 124.
https://doi.org/10.1016/S0377-0427(02)00816-6
Cited in this article [1]
Li K P , Yang T , Jiang W , et al. Isogeometric boundary element method for isotropic damage elastic mechanical problems. Theoretical and Applied Fracture Mechanics, 2023, 124: 103802.
https://doi.org/10.1016/j.tafmec.2023.103802
Cited in this article [1]
Lin B , Ma Y , Wang C S . A Lawson-time-splitting extended Fourier pseudospectral method for the Gross-Pitaevskii equation with time-dependent low regularity potential. Journal of Computational Physics, 2024, 512: 113133.
https://doi.org/10.1016/j.jcp.2024.113133
Cited in this article [1]
Liu Y , Sen M K . Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes. Bulletin of The Seismological Society of America, 2011, 101 (1): 141- 159.
https://doi.org/10.1785/0120100041
Cited in this article [3]
Liu Y . Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling. Geophysical Journal International, 2014, 197 (2): 1033- 1047.
https://doi.org/10.1093/gji/ggu032
Cited in this article [2]
Lu Y M , Yang J X , Zhang J F , et al. Traveltime calculation for qP and qSV waves based on fast fitting algorithm in 2D TTI media. Chinese Journal of Geophysics, 2025, 68 (5): 1911- 1921.
https://doi.org/10.6038/cjg2024R0795
Saenger E H , Gold N , Shapiro S A . Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion, 2000, 31 (1): 77- 92.
https://doi.org/10.1016/S0165-2125(99)00023-2
Cited in this article [2]
Wang C Q , Wu G C , Yang L Y . Finite-difference numerical simulation method for two-dimensional scalar waves in a 25-point Laplace-Fourier domain. Progress in Geophysics, 2025, 40 (6): 2698- 2710.
https://doi.org/10.6038/pg2025HH0496
Wang Q, Cheng B J, Xu T J, et al. 2025. Two-dimensional elastic wave numerical simulation in dual-phase HTI porous media. Progress in Geophysics (in Chinese): 1-12, doi: 11.2982.p.20250627.1131.023.
Wei H , Tong S Y , Xin C Q , et al. Numerical simulation of 2D three-component surface waves in TI media based on the rotated staggered grid. Oil Geophysical Prospecting, 2024, 59 (5): 1022- 1036.
https://doi.org/10.13810/j.cnki.issn.1000-7210.2024.05.010
Xie J R , He B S . Spatial-temporal high-order rotated-staggered-grid finite-difference scheme of elastic wave equations for TTI medium. Journal of Computational Physics, 2024, 498: 112684.
https://doi.org/10.1016/j.jcp.2023.112684
Cited in this article [6]
Xu Y G , Liao J P , Zhou L , et al. Comparing the adaptability of three different staggered-grids for the simulation of 3D anisotropic fractured media and improving the Lebedev method. Chinese Journal of Geophysics, 2023, 66 (3): 1164- 1179.
https://doi.org/10.6038/cjg2022Q0089
Yan H Y , Xu T . Suppressing spatial dispersion of seismic finite-difference modeling with the improved pix2pix algorithm. Journal of Computational Physics, 2024, 511: 113129.
https://doi.org/10.1016/j.jcp.2024.113129
Cited in this article [1]
Yang L , Yan H Y , Liu H . Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media. Journal of Applied Geophysics, 2015, 122: 40- 52.
https://doi.org/10.1016/j.jappgeo.2015.08.007
Cited in this article [7]
Yang L , Yan H Y , Liu H . An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling. Journal of Applied Geophysics, 2017, 138: 161- 171.
https://doi.org/10.1016/j.jappgeo.2017.01.020
Cited in this article [2]
Zhang J H , Yao Z X . Optimized finite-difference operator for broadband seismic wave modeling. Geophysics, 2013, 78 (1): A13- A18.
https://doi.org/10.1190/geo2012-0277.1
Cited in this article [3]
Zhang O M , Schmitt D R . An optimized 2D/3D finite-difference seismic wave propagator using rotated staggered grid for complex elastic anisotropic structures. Computers & Geosciences, 2025, 196: 105850.
https://doi.org/10.1016/j.cageo.2024.105850
Cited in this article [1]
Zhao M L , Shi J Y , Wang L Q . A three-dimensional Petrov-Galerkin finite element interface method for solving inhomogeneous anisotropic Maxwell's equations in irregular regions. Computers & Mathematics with Applications, 2023, 152: 364- 377.
https://doi.org/10.1016/j.camwa.2023.10.035
Cited in this article [1]
Zhong L , Ma S F , Joka D L . Meshless method for delay partial differential equations with piecewise continuous arguments. Chinese Journal of Computational Mechanics, 2021, 38 (2): 160- 165.
https://doi.org/10.7511/jslx20191217001
Zhou H Y , Liu Y , Wang J . Time-space domain scalar wave modeling by a novel hybrid staggered-grid finite-difference method with high temporal and spatial accuracies. Journal of Computational Physics, 2022, 455: 111004.
https://doi.org/10.1016/j.jcp.2022.111004
Cited in this article [1]
Zhou X H , Huo S D , Liang Y , et al. Finite-difference method for modeling the surface wave propagation with surface topography in anisotropic-viscoelastic media. Journal of Applied Geophysics, 2023, 217: 105161.
https://doi.org/10.1016/j.jappgeo.2023.105161
Cited in this article [1]
芦 永明 , 杨 建勋 , 张 剑锋 , 等. 基于快速拟合算法的二维TTI介质qP波和qSV波走时计算. 地球物理学报, 2025, 68 (5): 1911- 1921.
https://doi.org/10.6038/cjg2024R0795
Cited in this article [1]
王 超群 , 吴 国忱 , 杨 凌云 . 25点Laplace-Fourier域二维标量波有限差分数值模拟方法. 地球物理学进展, 2025, 40 (6): 2698- 2710.
https://doi.org/10.6038/pg2025HH0496
Cited in this article [1]
王啟, 程冰洁, 徐天吉, 等. 2025. 双相-HTI多孔介质二维弹性波数值模拟. 地球物理学进展. 1-12, doi: 11.2982.p.20250627.1131.023.
Cited in this article [1]
魏 皓 , 童 思友 , 辛 成庆 , 等. 基于旋转交错网格的TI介质二维三分量面波模拟. 石油地球物理勘探, 2024, 59 (5): 1022- 1036.
https://doi.org/10.13810/j.cnki.issn.1000-7210.2024.05.010
Cited in this article [1]
徐 云贵 , 廖 建平 , 周 林 , 等. 三维各向异性裂缝介质正演模拟的三种交错网格适应性比较及Lebedev方法的改进. 地球物理学报, 2023, 66 (3): 1164- 1179.
https://doi.org/10.6038/cjg2022Q0089
Cited in this article [1]
钟 霖 , 马 淑芳 , 莱 蒙 . 无网格法求解一类分段连续型延迟偏微分方程. 计算力学学报, 2021, 38 (2): 160- 165.
https://doi.org/10.7511/jslx20191217001
Cited in this article [1]

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